An analysis of the rotational motion of a uniaxial satellite due to magnetic and gravitational torques is presented. The rotational motion of a spinning rigid body responding to these torques, averaged over arbitrary portions of an eccentric orbit, can be described by an autonomous system of nonlinear differential equations. From this the phase trajectory described by the spin vector is obtained to show that the motion is periodic in the phase space fixed to the orbit plane. Poincare's method has been employed to analyze the perturbation effects of the gravitational torque on the periodic motion due to the dominant magnetic torque. It is found that the perturbed change in period is proportional to the projection of the spin vector on the characteristic vector about which the spin vector rotates. The approximate solution for the perturbed motion is also obtained as the coefficient of the power-series expansion in the small parameter representing the effect of the gravitational torque. PIN stabilization for attitude control of Earth satellites aims to keep the spin axis inertially fixed, by utilizing the principle of conservation of angular momentum. In practice, however, long-term drift of the spin axis is inevitable, due to various unintended perturbing torques which exist in the space environment. But it is possible to make a purposeful use of these disturbances as torques to perform attitude maneuvers. One of the well-established methods which take advantage of the environment is a magnetic torquing method, which utilizes interaction of the Earth's magnetic field with a satellite's magnetic moment. This method, because of its simplicity and reliability, has been widely used with success on a number of low to medium altitude satellites. Beletsky1 was first to study the problem of the rotational motion of a uniaxial satellite in a circular orbit influenced by perturbing torques such as those produced by aerodynamic and gravitational factors. He introduced into the equations of motion for the angular momentum vector a term corresponding to the perturbation produced by the nodal regression of the orbit. However, the theoretical analysis of the rotational motion was, for the most part, carried out relative to the nonregressing orbit. The effects of the nodal regression were studied by employing a numerical approach. Later Beletsky,2'3 Colombo,4 and Holland5 developed analytical methods for predicting the motion of the angular momentum vector of uniaxial and triaxial rigid bodies relative to the regressing orbit. In so doing, they achieved good agreement with the observed motions of the Sputnik III, the Explorer, and the Pegasus satellites which are under the dominant effect of the gravitational torque. In all of the aforementioned references, the external torques acting on the satellites are averaged over an entire orbit, because their interest is chiefly in the prediction of attitude variations of the satellites without special means for attitude control. In Ref. 6 and also here, we have treated external torques as mean torques averaged over arbitrary portions of the satellite orbit. This treatment is essential in the establishing of command